Music theory has traditionally been studied by analyzing relationships between major and minor tonalities based on a tonal center, or a “root” note. In a traditional harmonic system of understanding music, a composer understands the relationship between major, minor and dominant chords and uses this framework as a way to create music that makes sense to the composer and listener. Music, however, often finds a way to transcend traditional theoretical boundaries while still appealing to a listener. Even earlier Western music, written by composers like J. S. Bach of the Baroque period, at times crossed the boundaries of traditional music theory and used non-harmonic tones, while still producing meaningful melodies and harmonies.
More recently, music such as jazz and postmodern styles incorporate tonal intervals and chord changes in ways that defy traditional rules, yet still make musical sense. While non-traditional tonalities have harmonic relationships that may innately connect with a listener, an effective method for representing these non-traditional relationships in a way that a student of music can easily understand and visualize has not yet been developed.
Conventional sheet music notation, which includes notes on a musical staff written on a two dimensional sheet or display, does not provide a student or composer with the best means for understanding of the harmonic relationships between notes. Three dimensional representations of music can augment a musician's understanding of music theory. Human beings are designed to most effectively see the world in three dimensions. In terms of comprehension and creation, seeing is more effective than reading.
A system of representing music in three dimensions would allow a listener to not only ‘see’ music, but also provide a framework where musical notes can belong to specific spatial key centers. A key center, expressed in 3D, could provide a means for effective analysis and richer composition.
Prior attempts to represent musical harmony in three dimensions have not been widely adopted in music teaching and analysis. These attempts have fallen short in terms of providing coherent systems useful for the purpose of music analysis. Dmitri Tymoczko's The Geometry of Musical Chords, the Riemannian Tonnetz, Tod Machover's HyperScore and other methods of representing music in three dimensions have only provided ways to represent music in either subjective ways, which impose criteria that do not relate to music or harmony and use mathematical equivalences which ignore harmonic functionality, or by following counterpoint considerations that relate to idiomatic style rather than to functional harmony. Therefore, there is a need for different systems and methods of musical notation that allow music to be visualized three dimensionally in new ways.